A diffusion approximation for the ruin function of a risk process with compounding assets

Abstract

The traditional theory of collective risk is concerned with fluctuations in the capital reserve {Y(t): t ?O} of an insurance company. The classical model represents {Y(t)} as a positive constant x (initial capital) plus a deterministic linear function (cumulative income) minus a compound Poisson process (cumulative claims). The central problem is to determine the ruin probability ψ(x) that capital ever falls to zero. It is known that, under reasonable assumptions, one can approximate {Y(t)} by an appropriate Wiener process and hence ψ(.) by the corresponding exponential function of (Brownian) first passage probabilities. This paper considers the classical model modified by the assumption that interest is earned continuously on current capital at rate β > O. It is argued that Y(t) can in this case be approximated by a diffusion process Y*(t) which is closely related to the classical Ornstein-Uhlenbeck process. The diffusion {Y*(t)}, which we call compounding Brownian motion, reduces to the ordinary Wiener process when β = O. The first passage probabilities for Y*(t) are found to form a truncated normal distribution, which approximates the ruin function ψ(.) for the model with compounding assets. The approximate expression for ψ(.) is compared against the exact expression for a special case in which the latter is known. Assuming parameter values for which one would anticipate a good approximation, the two expressions are found to agree extremely well over a wide range of initial asset levels.     

The Campus Parking Game: A Demonstration of Price Discrimination and Efficiency

This article presents a classroom game that allows students to directly experience the welfare improvements that can result from price discrimination. The demonstration uses a very familiar decision-making scenario, campus parking, to introduce the concept of price discrimination as well as reinforce the concepts of opportunity cost, consumer surplus, and search costs. This game can be used in a variety of classes, including principles, intermediate theory, industrial organization, or environmental economics, and can be conducted in a 50-minute class period with follow-up discussion in the next class.     

Impact of behavioral health problems on access to care and health services utilization

Access to specialists for treatment of behavioral health problems has become restricted in this era of capped budgets and reductions in Medicare and Medicaid reimbursement. Patients with multiple mental health problems may face additional barriers to obtaining needed health care services. The study's aim was to measure the impact of behavioral health problems on access to care and health services utilization for veterans and non-veterans and to determine the contribution of health system characteristics in the prediction of self-reported health services utilization. The study sample consisted of Vietnam veterans who participated in both the Vietnam Drug User Study (September 1971 Army discharges) and the Vietnam Era Study (25-year follow-up) (N=642), as well as a non-veteran cohort (N=197).     

Water-Based Recreational Benefits of Conservation Programs: The Case of Conservation Tillage on U.S. Cropland

Conservation programs are a significant part of farm legislation. The recent farm bill increases funding of conservation programs. One result will likely be the increased adoption of basic environmentally benign farming practices, such as conservation tillage. This would lead to improvements in surface water quality. In this paper, we examine the magnitude of the nonmarket use value benefits of these improvements. The findings indicate that moderate to widespread adoption of practices such as conservation tillage would result in significant nonmarket benefits.     

Method for identifying strategic objectives in strategy maps

This paper describes a simple tool for identifying strategic objectives as part of the design of strategy maps, based on the balanced scorecard, and meant to be used in organisations to establish performance indicators. To design the tool, a number of companies that implemented the balanced scorecard were analysed, in order to obtain their methodologies to create strategy maps. Three types of methods were found, different from each other in the way the strategic objectives are defined. By studying the benefits and drawbacks of the three methods, a simple, method was obtained. Basically, the method identifies general and specific strategic objectives and uses a modified SWOT (strengths, weaknesses, opportunities, threats) analysis. This paper also makes an analysis of the type of strategic objectives that the studied companies defined as part of the balanced scorecard implementation process.